- Virtual large cardinal principles
This is a talk at the Harvard Logic Colloquium, Cambridge, November 8, 2017.

- Filter games and Ramsey-like cardinals
This is a talk at the CUNY Set Theory Seminar, October 20, 2017.

- A model of second-order arithmetic with the choice scheme in which $\Pi^1_2$-dependent choice fails
This is a talk at the Kurt Gödel Research Center Research Seminar in Vienna, Austria, May 18, 2017.

- Computable processes which produce any desired output in the right nonstandard model
This is a talk at the special session “Computability Theory: Pushing the Boundaries” of 2017 AMS Eastern Sectional Meeting in New York, May 6-7.

- Virtual Set Theory and Generic Vopěnka’s Principle
This is a talk at the VCU MAMLS Conference in Richmond, Virginia, April 1, 2017.

- A countable ordinal definable set of reals without ordinal definable elements
This is a talk at the CUNY Set Theory Seminar, February 10, 2017.

- A set-theoretic approach to Scott’s Problem
This is a talk at the National University of Singapore Logic Seminar, October 19, 2016.

- Generic Vopěnka’s Principle at YST2016
This is a talk at the Young Set Theory 2016 Conference in Copenhagen, Denmark, June 13-17, 2016.

- Generic Vopěnka’s Principle
This is a talk at the Rutgers Logic Seminar in New Jersey, May 2, 2016.

- Computable processes can produce arbitrary outputs in nonstandard models
This is a talk at the CUNY MOPA Seminar in New York, April 13, 2016.

- Virtual large cardinals
This is a talk at Set Theory Day in New York, March 11, 2016.

- Ehrenfeucht principles in set theory
This is a talk at the British Logic Colloquium in Cambridge, UK, September 2-4, 2015.

- Indestructible remarkable cardinals
This is a talk at the 5th European Set Theory Conference in Cambridge, UK, August 24-28, 2015.

- An introduction to nonstandard models of arithmetic
This is a talk at the Virginia Commonwealth University Analysis, Logic and Physics Seminar, April 24, 2015.

- Remarkable Laver functions
This is a talk at the CUNY Set Theory Seminar, February 27, 2015.

- Kelley-Morse set theory and choice principles for classes
This is a talk at the SoTFoM II (Symposia on the Foundations of Mathematics) conference in London, UK, January 12-13, 2015.

- Choice schemes for Kelley-Morse set theory
This is a talk at the Colloquium Logicum Conference in Munich, Germany, September 4-6, 2014.

- Incomparable $\omega_1$-like models of set theory
This is a talk at the Connecticut Logic Seminar, March 31, 2014.

- Introduction to remarkable cardinals
This is a talk at the CUNY Set Theory Seminar, March 14, 2014.

- Ramsey cardinals and the continuum function
This is a talk at the CUNY Logic Workshop, February 14, 2014.

- A Jonsson $\omega_1$-like model of set theory
This is a talk at the CUNY Set Theory Seminar, November 15, 2013.

- Embeddings among $\omega_1$-like models of set theory
This is a talk at the CUNY Set Theory Seminar, October 4, 2013.

- Models of $\rm{ZFC}^-$ that are not definable in their set forcing extensions
This is a talk at the CUNY Set Theory Seminar, May 4, 2012.

- Julia sets and the Mandelbrot set
This is a talk at the City Tech Math Club, April 19, 2012.

- Indestructibility for Ramsey cardinals
This is a talk at the Rutgers Logic Seminar, April 2, 2012.

- An iPhone app for a nonstandard model of number theory?
This is a talk at the City Tech C-LAC (Center for Logic, Algebra, and Computation) Seminar, February 14, 2012.

- Forcing and gaps in $2^\omega$
This is a talk at the CUNY Set Theory Seminar, December 2nd, 2011.

- A natural model of the multiverse axioms
This is a talk at the MIT Logic Seminar, April 8, 2010.

- Gödel’s Proof
This is a talk at the United States Military Academy at West Point Mathematics Seminar, January 20, 2010.

- Making strong cardinals indestructible by $\leq\kappa$-weakly closed Prikry forcing
This was a talk at the CUNY Set Theory Seminar sometime in 2009.

### Recent Writing

- Virtual large cardinal principles
- Filter games and Ramsey-like cardinals
- The exact strength of the class forcing theorem
- A model of the generic Vopěnka principle in which the ordinals are not $\Delta_2$-Mahlo
- A model of second-order arithmetic with the choice scheme in which $\Pi^1_2$-dependent choice fails

### Mathoverflow Activity

- Comment by Victoria Gitman on Does Con(ZF + Reinhardt) really imply Con(ZFC + I0)?@Stefan For some reason, I cannot click on the link.Victoria Gitman
- Comment by Victoria Gitman on Cofinality of $j(\kappa)$ for a measurability embedding $j:V\to M$ with critical point $\kappa$@AsafKaragila I edited the question to make it clearer. Maybe I will ask your version as a follow-up if you don't ask it first :).Victoria Gitman
- Comment by Victoria Gitman on Cofinality of $j(\kappa)$ for a measurability embedding $j:V\to M$ with critical point $\kappa$@AsafKaragila I should have done a better job stating my question clearly. I wanted to know precisely what Yair answered: whether there are models where $\text{cf}(j(\kappa))$ is smaller than the size of $j(\kappa)$. Your interpretation of the question is very interesting as well, but I think much harder to answer.Victoria Gitman

- Comment by Victoria Gitman on Does Con(ZF + Reinhardt) really imply Con(ZFC + I0)?
### Cantor’s Attic

- Constructible universeImplications, equivalences, and consequences of $0^\#$'s existence ← Older revision Revision as of 11:26, 14 December 2017 Line 63: Line 63: If $0^\#$ exists then: If $0^\#$ exists then: −* $\aleph_\omega$ is [[stable]] in $L$ and so $0^\#$ also corresponds to the set of the Gödel numberings of first-order formulas $\varphi$ such that $L\models\varphi(\aleph_0,\aleph_1...\aleph_n)$+* $L_{\aleph_\omega}\prec […]Julian Barathieu
- Axiom of determinacy← Older revision Revision as of 11:13, 14 December 2017 Line 100: Line 100: * Every uncountable cardinal $Julian Barathieu
- Upper attic← Older revision Revision as of 11:07, 14 December 2017 Line 30: Line 30: * [[zero dagger| $0^\dagger$]], $j:L[U]\to L[U]$ cardinal * [[zero dagger| $0^\dagger$]], $j:L[U]\to L[U]$ cardinal * '''[[measurable]]''' cardinal, [[weakly measurable]] cardinal, singular [[Jonsson|Jónsson]] cardinal * '''[[measurable]]''' cardinal, [[weakly measurable]] cardinal, singular [[Jonsson|Jónsson]] cardinal −* [[Jonsson | Jónsson]] cardinal, [[Rowbottom]] cardinal, '''[[Ramsey]]''' cardinal, [[strongly Ramsey]] […]Julian Barathieu
- Strongly compactDiverse characterizations ← Older revision Revision as of 08:57, 14 December 2017 Line 18: Line 18: A cardinal $\kappa$ is $\theta$-strongly compact if and only if there is an [[elementary embedding]] $j:V\to M$ of the set-theoretic universe $V$ into a transitive class $M$ with critical point $\kappa$, such that $j''\theta\subset s\in M$ for some […]Julian Barathieu
- Supercompact← Older revision Revision as of 21:12, 11 December 2017 Line 10: Line 10: One can see the equivalence of the two formulations by first considering the ultrafilter $U$ arising from the [[seed]] $j''\theta$, so that $X\in U\iff j''\theta\in j(X)$. It is easy to check that $U$ is a normal fine measure on $\mathcal{P}_\kappa(\theta)$. Conversely, […]Julian Barathieu

- Constructible universe